Presents the first of two articles examining Alfred North Whitehead's notion of the rhythm of the university, discussing the rhythm of teaching and learning, the importance of academic freedom to an imaginative faculty, and the relationship between Whitehead's own pedagogy and his considerable administrative practice. The paper's purpose is to…

We comment on the paper "The co-emergence of machine techniques, paper-and-pencil techniques, and theoretical reflection: A study of CAS use in secondary school algebra" by Carolyn Kieran and Paul Drijvers. We look at aspects of Kieran and Drijvers' analysis with regard to "task-technique-theory" in the light of a model of abstraction in context…

As engineers gain experience and become experts in their domain, the structure and content of their knowledge changes. Two studies are presented that examine differences in knowledge representation among freshman and senior engineering students. The first study examines recall of mechanical devices and chunking of components, and the second…

People spontaneously discover new representations during problem solving. Discovery of a mathematical representation is of special interest, because it shows that the underlying structure of the problem has been extracted. In the current study, participants solved gear-system problems as part of a game. Although none of the participants initially…

The author believes that very young children are able to understand the abstract concept of peace. In her primary classroom she introduces the concept of peace to the children in a low energy environment with low lights, and soft music. When children feel at peace in their hearts, they relate peacefully to those around them. She begins with the…

A number of thought experiments are cited, some well-known, some not. These illustrate the power of thought experiments. Other examples are given that show some of the dangers. As well as examples from the science, some examples of visual reasoning from mathematics are also presented, again with an eye to illustrating their promise and perils.…

Cross-sectional and longitudinal data from students as they advance through the middle school years (grades 6-8) reveal insights into the development of students' pattern generalization abilities. As expected, students show a preference for lower-level tasks such as "reading the data," over more distant predictions and generation of abstractions.…

This study examined test-related experiences of enjoyment, anger, anxiety, and boredom in a sample of 2059 German school students (50% female) from grade 6, and how they relate to students' abstract reasoning ability (ARA). Emotions were assessed immediately before, during, and after a mathematics achievement test. Analysis of variance showed that…

The purpose of this study was to examine the Wechsler Intelligence Scale for Children-Revised (WISC-R) profiles of two treatment populations and present a theoretical rationale for using adventure therapy. Data for the first group were obtained from the psychological testing records of 150 randomly selected inpatients (81 males, 69 females)…

A discussion focusing on the abstractness of analysis in phonology, debated since the 1960s, describes the issue, reviews the literature on the subject, cites specific natural language examples, and examines the extent to which the issue has been resolved. An underlying representation is said to be abstract if it is different from the derived one,…

A unit on animals was taught to 64 preschool children (44 in an experimental group and 20 in a control group). Children in the experimental group were taught nine major concepts over four levels of abstraction (designated as superordinate, intermediate, subordinate, or particular levels). Each concept was presented by means of an advance organizer…

The Wechsler Adult Intelligence Scale was administered to 30 male criminally insane patients and 15 violent convicts. The latter had similar subtest score configurations and the mean similarities ratio score for the violent group was significantly lower than that of the nonviolent group. (Author/SE)

Suggests that the intellectual school of thought that emphasizes the strength of black families has misled the black movement away from an attack on the suffering of blacks in their family situation and related conditions; i.e. the psychological effects and social destruction of unemployment and under employment of black males. (Author/AM)

Analogical reasoning is frequently used in acquisition of mathematical concepts. Concrete representations used to teach mathematics are essentially analogs of mathematical concepts, and it is argued that analogies enter into mathematical concept acquisition in numerous other ways as well. According to Gentner's theory, analogies entail a…